A father's present age is twice the sum of the ages of his two children. After 20 years, his age will equal the sum of their ages then. Find the father's present age.
\(40\) years.
Step 1: Let the sum of the children's present ages be \(C\).
Step 2: Let the father's present age be \(F\).
Step 3: According to the question, the father's age is twice the sum of the children's ages.
So, \(F = 2C\).
Step 4: After 20 years:
The father's age will be: \(F + 20\).
The children's ages together will be: \(C + 20 + 20 = C + 40\).
(Because there are two children, each gets 20 years added.)
Step 5: At that time, father's age will equal the children's total age.
So, \(F + 20 = C + 40\).
Step 6: Now substitute \(F = 2C\) into the equation:
\(2C + 20 = C + 40\).
Step 7: Solve step by step:
\(2C + 20 = C + 40\)
Subtract \(C\) from both sides: \(C + 20 = 40\)
Subtract 20 from both sides: \(C = 20\)
Step 8: Father's present age:
\(F = 2C = 2 \times 20 = 40\).
Final Answer: The father is 40 years old.